School police would have to call their own dispatchers, who would then contact Boston police for armed backup — a relay of information they contend could cost precious minutes in saving lives. “They don’t have the proper tools to confront the things that they might confront in the school and indeed the things they confront every day,” said Alfred Gordon, a Boston lawyer who represents the ranking officers in the school police force. “Would we be prepared to face something like what happened in Newtown? I don’t know. I wish we could say with ultimate authority that we are, but I don’t know.” City officials have reassured parents that their children are safe in school. But Matthew Wilder, a School Department spokesman, said Superintendent Carol R. Johnson is planning to look into equipping school police with bulletproof vests and into whether it makes sense for the school police’s radio system to be connected directly with that of the Boston Police Department. School police, who are trained to conduct emergency lock-downs of buildings, have long sought the authority to carry guns, but Johnson and Mayor Thomas M. Menino oppose the idea.